Review on Optimization of Drill and Blast Parameters Using Empirical Fragmentation Modelling (Kuz-Ram Model)

1. Review on
Optimization of Drill and Blast Parameters Using
Empirical Fragmentation Modelling (Kuz-Ram Model)
Elias Kassahun (李安 )

2. Content of the discussion
 Introduction
 Material and method used
 Rock characterization
 Expected Result and Discussion
 Performance of Block (from exemplary data)
 Conclusion
 Reference

3. I. Introduction
❖ The primary purpose of blasting is to fragment rock, and there are significant rewards for
delivering a fragmentation size range that is not only well suited to the mining system it
feeds but also minimizes unsaleable fractions and enhances the value of what can be sold.
❖ The outcome of blasting operations are determined by a number of indices or parameters,
which can either, be controllable or uncontrollable.
❖ The controllable parameters are basic blast design parameters, which can be varied to
adjust the outcome of the operations, and this produce close to accurate results assuming
the rock mass is homogenous and without discontinuities.
❖ But the uncontrollable ones are inherent properties of the rock, geological structures,
usually defined by fracture distributions, need to be factored and included in the blast
design.

4. ❖ According to (Hustrulid, 1999)
The controllable parameters are classified in the following groups:
A. Geometric: Diameter, charge length, burden, spacing etc.
B. Physicochemical or pertaining to explosives: Types of explosives, strength, energy,
priming systems, etc.
C. Time: Delay timing and initiation sequence.
The uncontrollable factors includes but are not limited to :
➢ Geology of the deposit,
➢ Rock strength and properties,
➢ Presence of water,
➢ Joints, etc.

5. ➢ The cost of drilling and blasting operations greatly contributes to the “high cost trends
of the overall mining operations” (Anon., 2014; Anon., 2012, Palangio et al., 2005 and
Bozic, 1998).
➢ Drilling, one of the critical and important operations of every hard rock mine
contributes about 15% of the overall mining cost in some mining operations (Gokhal,
2010).
➢ However, reducing cost through optimization of drill and blast geometric parameters
have barely been considered.
➢ Several factors affect the cost of fragmenting any piece of in-situ rock. These factors
include but not limited to blast geometric parameters and pattern; explosive type,
density and costs; labor; oversize (relative boulders), toes and geological nature of the
formation

6. ❖ Various models have been put forward over the years, attempting to predict the size
distribution resulting from particular blast designs. The approaches fall into two broad
camps:
1. Empirical modelling, which infers finer fragmentation from higher energy input, and
2. Mechanistic modelling, which tracks the physics of detonation and the process of energy
transfer in well-defined rock for specific blast layouts, deriving the whole range of
blasting results.

7. II. Material and method used
Kuz-ram fragmentation method
➢ Characteristics of blasted rock such as fragment size, volume and mass are fundamental
variables affecting the economics of mining operations, and are in effect the basis for
evaluating the quality of a blast (Bozic, 1998).
➢ The properties of fragmentation, such as size and shape, are very important information
for the optimization of production drilling and blasting operations.
➢ In recent years empirical methods for predicting the fragmentation from a given
structural geology, rock type, explosive, and blast pattern have become better and more
useful.
➢ Empirical prediction of expected fragmentation is most often done using the Kuz-Ram
model.
➢ The basic strength of the model lies in its simplicity in terms of the ease of garnering
input data, and in its direct linkage between blast design parameters and rock
fragmentation (Cunningham, 2005).

8. Cont…
➢ Using this approach, a rock factor that describes the nature and geology of the rock is
calculated. A uniformity index is also obtained that characterizes the
explosive loading, the blast pattern type and dimensions.
➢ This allows a characteristic size and size distribution to be determined according to the
Rosin-Rammler procedure. There are three key equations of the Kuz-Ram model
(Cunningham, 2005).
➢ Kuznetsov equation
Xm=AK-0.8
Q1/6
(115/RWS)19/20
Where Xm = mean particle size, cm; A = rock factor varying between 0.6 and 22,
depending on hardness and structure]; K = powder factor, kg explosive per cubic meter of
rock; Q = mass of explosive in the hole, kg; and RWS = Relative Weight Strength.

9. Rock characterization: factor A
It is always difficult to estimate the real effect of geology, but the following routine addresses
some of the major issues in arriving at the single rock factor A, defined as
A = 0.06 (RMD + RDI + HF)……………………………………….. 4
where RMD is the rock mass description, RDI is the density influence and HF is the hardness
factor, the figures for these parameters being derived as follows.
4.1.1 RMD
A number is assigned according to the rock condition:
❖Powdery/friable = 10;
❖Massive formation (Joints further apart than blasthole) = 50;
❖vertically jointed – derive jointed rock factor (JF) as follows:
JF = (JCF * JPS) + JPA ………………………………………………5
Where JCF is the joint condition factor, JPS is the joint plane spacing factor and JPA is the joint
plane angle factor.
4.1.1.1 Joint condition factor (JCF)
Tight joints=1
Relaxed joints=1.5
Gouge-filled joints=2.0

11. 4.1.1.2 Vertical joint plane spacing factor (JPS)
As illustrated in Figure 1, this factor is partly related to the absolute joint spacing, and partly to
the ratio of spacing to drilling pattern, expressed as the reduced pattern, P:
P = (B x S)0.5 ……………………………………………6
where B and S are burden and spacing, m. The values of JPS are as follows for the joint spacing
ranges:
✓ joint spacing < 0.1 m, JPS = 10 (because fine fragmentation will result from close joints);
✓ joint spacing = 0.1–0.3 m, JPS = 20 (because unholed blocks are becoming plentiful and
large);
✓ joint spacing = 0.3 m to 95% of P, JPS = 80 (because some very large blocks are likely to be
left);
✓ joint spacing > P, 50 (because all blocks will be intersected).
Clearly, if the joint spacing and the reduced pattern are both less than 0.3 m, or if P is less than
1 m, then this algorithm could produce strange results. In the original derivation, the index was
linked to the maximum defined oversize dimension, but this is clearly not an appropriate input
and has been omitted.

12. 4.1.1.3 Vertical joint plane angle (JPA)
Dip out of face = 40
Strike out of face = 30
Dip into face = 20
‘Dip’ here means a steep dip, >30m. ‘Out of face’ means that extension of the joint plane from
the vertical face will be upwards. This is a change from the 1987 paper and is supported by
Singh & Sastry (1987), although the wording in the latter is slightly confused and requires
careful interpretation.
4.1.2 RDI is the Rock Density Influence = (0.25ρ - 50)
where ρ is density of the rock in kg/m3;
4.1.3 Hardness factor (HF)
If Y < 50, HF = Y/3
If Y > 50, HF = UCS/5
where Y = elastic modulus, GPa; UCS = unconfined compressive strength, MPa.
This distinction is drawn because determining the UCS is almost meaningless in weak rock
types, and a dynamic modulus can be more easily obtained from wave velocities.

13. Cont…
Rosin-Rammler equation:
The Rossin-Ramlers equation for percentage passing is determine in two equation. This is
also important in characterizing muck pile size distribution (Faramarzi, et al., 2013).
%passing=100-[100×e-0.693× [mesh size/Xm]
n
]………………………..2a
Rx=exp[-0.693(x/xm)n]……………………………………………..2b
Where Rx = mass fraction retained on screen opening x; and n = uniformity index, usually
between 0.6 and 2.2 . Percentage (%) passing represents the percentage of material that will
pass through a screen of a particular mesh size (X).

14. Uniformity equation
where B= burden, m; S = spacing, m; d= hole diameter, mm; W= standard deviation of
drilling precision, m; L = charge length, m; BCL = bottom charge length, m; CCL = column
charge length, m; and H= bench height, m.

15. III. Expected Result and Discussion (Optimization of the Drill and
Blast Parameters for the Mine )
 Drilling and blasting operations of the mine were closely studied to identify alternative
geometric parameters for blasting based on the Kuz-Ram fragmentation model that
reduces the total cost of blasting.
 Other technical parameters that would significantly reduce costs and improve productivity,
whilst maintaining the desired rock fragmentation and wall control were also considered.
 To assess the blast performance and further generate appropriate sets of geometric
parameters for drilling and blasting in a surface mine, it is recommended to use the Kuz-
Ram fragmentation model which is the best estimator (Cunningham, 1983; 1987; 2005) of
geometric parameters.
 It is also a tool for examining how different parameters could influence blast performance.
The major factors for selecting the optimum and appropriate set of geometric drill and
blast parameters of a mine include the total cost/BCM blasted, and the desired mean
fragmentation size.

16. Performance of Block
 It is observed in Table 1, that by adopting Proposal 1 as an alternative for ore zones in
Block A, the Powder Factor (PF) would reduce fairly from 0.76 to 0.73 kg/m3, the mean
fragment size increases slightly from 27.06 to 27.44 cm, and the total cost per BCM of
drilling and blasting would reduce from $1.13/m3 to $1.07/m3. The fragmented BCM per
blasthole would considerably increase by 25%, an added advantage for the mine.
 Similarly, in blasting the waste zone of Block (Table 1), the set of drill and blast
geometric parameters for Proposal 1 give a better alternative to the current practice. If
the mine is to adopt Proposal 1 for blasting the waste zones in Block A pit, the PF would
reduce from 0.58 to 0.52 kg/m3, the mean rock fragment size would increase from 33.5
cm to 36.8 cm and the total cost per BCM of drilling and blasting would reduce from $
0.87/m3 to $ 0.77/m3. The blasted BCM per blasthole using the proposed alternative
geometric parameters for the waste zones of Block A pit would increase by 12.5%.

17. IV. Conclusion
 Several factors including on-bench geometric parameters, technical explosive data and
desired fragmentation sizes influence the cost trends in the drilling and blasting
operations of a mine.
 The Kuz-Ram fragmentation model was used as a tool for experimenting with various
blast geometric parameters to improve on drill and blast performance of the mine.
 The blast performance was measured in terms of the Powder Factor (PF),the mean
fragment size and the volume of blasted material per blasthole in the sample block.
 The total cost of drilling and blasting in the three pits and the cost savings from the
proposed blast parameters over the mine’s current parameters for ore and waste zones
were assessed.

18. V. Reference
 Jethro Michael Adebola, Ogbodo David, and Ajayi Peter Elijah.O, Rock Fragmentation
Prediction using Kuz-Ram Model, ISSN 2224-3216 (Paper) ISSN 2225-0948 (Online)
Vol.6, No.5, 2016
 Cunningham, C.V.B. (2005) The Kuz-Ram Model-20 years on. Brighton Conference
Proceedings.
 Afum B. O. and Temeng V. A. (2015), “Reducing Drill and Blast Cost through Blast
Optimizations – A Case Study”, Ghana Mining Journal, Vol. 15, No. 2, pp. 50 - 57.
 Ninepence, J. B, Appianing, E. J. A. , Kansake, B. A. , and Amoako, R. , “Optimisation of
Drill and Blast Parameters Using Empirical Fragmentation Modelling”, 4th UMaT Biennial
International Mining and Mineral Conference
 Afum B. O. and Temeng V. A. (2015), “Reducing Drill and Blast Cost through Blast
Optimisation – A Case Study”, Ghana Mining Journal, Vol. 15, No. 2